A communication system generally uses channel coding to improve reliability of data transmission and ensure quality of communication. A polar (Polar) code is a theoretically-proved good code which may obtain a Shannon capacity and has low encoding and decoding complexities (the encoding and decoding complexities are O (N log N), where N is a code length). When a code length of the Polar code is large, good performance can be obtained by using successive-cancellation (Successive-Cancellation, SC) decoding, such as SC decoding and SC-List decoding, the SC-List decoding greatly improves performance of the SC decoding, which is close to the best maximum-likelihood decoding (maximum-likelihood, ML for short) performance. However, when the Polar code is short or is of a medium length, performance of the proposed SC decoding and SC-list decoding is not outstanding, and the performance needs to be improved. That is to say, the SC decoding can achieve good performance which approaches Shannon limit in a case where the code length N is very long; but when N is relative short or is of a medium length, the performance of the SC decoding of the Polar code does not exceed performance of a Turbo and a low density parity check code (Low Density Parity Check Code, LDPC code for short), thus the decoding performance needs to be further improved.
For this purpose, the industry insider has proposed an improved coding method for improving subsequent decoding performance, for instance, CRC coding and Polar coding are subject to cascade connection so as to improve minimum code distance of a final Polar code, thereby achieving an improvement in the performance of the SC decoding/SC-list decoding of the Polar code when the code length N is relatively short or is of a medium length. A matrix generated by the above-described CRC coding method has a following form: GCRC=[I PCRC].
However, a Polar code generating method using the cascaded CRC coding may not be able to improve minimum distance of entire codes; for instance, the Polar code cannot improve the minimum code distance under the CRC check code with some generator polynomial.